Select inner edge of solidified mesh
You will have to apply the Solidify modifier. This will generate the inner vertices.

Or you can do this without modifiers. Select your mesh, go into Edit mode. Select all the vertices you'd like to solidify and do one of the following:


hit Space, then type "Solidufy";
or press Ctrl+F > Solidify.


After execution of the operation you can adjust the thickness either pressing F6 or opening bottom of the N panel, where 'Last Operator' scroll located.